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CHAPTER 13 s ASYMMETRIC KEY CRYPTOGRAPHY
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Since RSA has been around longer than ECC, and mathematicians have had more time to look at attacks on RSA (Boneh 1999), we might say that RSA is better understood than ECC. Nevertheless, ECC has started making an impact in real-world security systems. For example, NIST, ANSI, and IEEE have standardized how ECC should be used for government, financial, and other types of systems. Also, while Certicom holds many patents surrounding ECC, NSA has purchased a blanket license for the use of ECC in protecting government information. The mathematics of ECC, as with RSA, are beyond the scope of this book. (Cryptography and Network Security: Principles and Practice, by W. Stallings, is a good source to learn about the mathematics of both RSA and ECC.) The key characteristic of ECC-based public key cryptography that is important from a systems standpoint is that it allows you to do public key operations using much smaller keys than RSA.
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13.4. Symmetric vs. Asymmetric Key Cryptography
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Symmetric key encryption using algorithms like DES, Triple DES, and AES are relatively efficient compared to asymmetric key cryptography because they do not require as many CPU cycles. This is due to their use of relatively simple, discrete logic operations, as compared to modular exponentiation in RSA. As a result, RSA ends up being about one thousand times slower than DES (Daswani and Boneh 1999). There are other trade-offs between the two algorithms as well. In a symmetric encryption algorithm, there is a concern that if Alice and Bob want to communicate, they would need to agree on a key beforehand. The key agreement problem may not be as significant in the asymmetric case because public keys can be published to everybody. However, there is still a problem with publishing public keys that we haven t addressed. Specifically, anyone can generate a public/private key pair, but the user s public key needs to be tied to the user s identity. Earlier in this chapter, we discussed an example in which Bob published his public key to a public directory. To keep things simple in our explanation as we introduced asymmetric cryptography, we left out one important detail. When Alice does a lookup in the public directory for Bob s public key, how does she know that someone is not impersonating Bob In particular, you can think of the public directory as a two-column table in which the first column is the name of a person, and the second column is that person s public key. If the public directory allows anyone to publish a public key without first verifying that person s identity, an attacker could masquerade as Bob by publishing a public key under Bob s name!
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13.5. Certificate Authorities
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To solve the problem discussed in the preceding section, we need to introduce a trusted third party called a certificate authority (CA) to verify people s identities. Specifically, the CA binds people s identities to their public keys. To accomplish this, a CA, for instance, authenticates Bob, and then digitally signs a statement called a public key certificate (or certificate, for short) saying that The public key for bob@learnsecurity.com is... (we cover digital signatures in 15). Certificates typically also specify an expiration date, such that the identity-topublic-key binding should not be trusted by default after the expiration date. A CA is also responsible for revoking keys and certificates. Sometimes, a user s private key is lost, compromised, or outright stolen prior to the expiration date in the certificate. In that
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CHAPTER 13 s ASYMMETRIC KEY CRYPTOGRAPHY
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case, the CA publishes a certificate revocation list (CRL) that specifies all of the keys that are revoked, or should not be trusted. Principals that need to encrypt data with public keys or verify digital signatures are expected to check CRLs for revoked keys as part of their processing. The CA, together with all of the corresponding hardware, software, services, and processes required to support public key encryption, decryption, digital signatures, and certificates, are often referred to as public key infrastructure (PKI).
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13.6. Identity-Based Encryption (IBE)
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In the RSA and ECC schemes described previously, Alice would need to acquire Bob s public key certificate before sending an encrypted message to him (or else she could not be sure that she would be encrypting with Bob s public key, and not that of an impostor). Alice would either have to request Bob s public key certificate from Bob, from a directory, or from the CA. Part of the reason for the existence of the public key certificate is that in both RSA and ECC, Bob s public key, kp, is a string of bytes that happens to satisfy the constraint F 1(F(m,kp),ks) = m, and the certificate binds kp to Bob s identity. However, if Bob s public key could instead be, say, his e-mail address (bob@learnsecurity. com), then Alice would not have to fetch Bob s public key certificate if she knows his e-mail address. Alice could simply encrypt the message she would like to send to Bob with his e-mail address. In this case, Bob s e-mail address is both his identity and his public key. To decrypt the message, Bob retrieves his private key from a private key generator (PKG) run by his company (learnsecurity.com), and applies his private key to the encrypted message. To successfully retrieve his private key, Bob authenticates to the PKG in much the same way that he would with a CA. However, in IBE, the PKG (in addition to Bob) knows his private key. Dan Boneh and Matt Franklin s Identity-Based Encryption from the Weil Pairing, describes a practical implementation of such an identity-based encryption scheme. Their scheme has been commercialized by Voltage Security (www.voltage.com), a startup company founded in 2002. Revocation works differently in IBE than in traditional PKI. In traditional PKI, the CA publishes a CRL. Over time, the length of a CRL grows, and must be downloaded before encrypting or verifying a signature to avoid using a revoked public key. In IBE, if we make the public key Bob s e-mail address concatenated with the current date (bob@learnsecurity.com || current-date), then the PKG simply will not provide Bob private keys corresponding to the public keys for those dates after which his key is revoked.
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